Problem: Simplify the following expression: $q = \dfrac{1}{7z} + \dfrac{1}{9z}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7z$ and $9z$ $\lcm(7z, 9z) = 63z$ $ q = \dfrac{9}{9} \cdot \dfrac{1}{7z} + \dfrac{7}{7} \cdot \dfrac{1}{9z} $ $q = \dfrac{9}{63z} + \dfrac{7}{63z}$ $q = \dfrac{9 +7}{63z}$ $q = \dfrac{16}{63z}$